Question

give the condition required for the figure to be a rhombus.
the figure is a rhombus if x =
(type an integer or a decimal.)

Explanation:

Step1: Recall rhombus diagonal property

In a rhombus, the diagonals bisect the angles. Also, adjacent angles in a rhombus are supplementary, but here, looking at the diagram (assuming the angle given is related to a right angle? Wait, maybe the diagonal forms a right angle? Wait, no—wait, in a rhombus, the diagonals are perpendicular bisectors? Wait, no, the diagonals bisect the angles. Wait, maybe the angle \( (6x + 6)^\circ \) is a right angle? Wait, no, maybe the figure is a rhombus, so the diagonals bisect the angles, and if it's a rhombus, maybe the angle here is 90? Wait, no, maybe the diagram shows that the diagonal creates an angle, and for it to be a rhombus, that angle should be 90? Wait, no, let's think again. Wait, maybe the figure is a rhombus, so the diagonals are perpendicular? Wait, no, in a rhombus, diagonals are not necessarily perpendicular unless it's a square, but no—wait, no, in a rhombus, diagonals are perpendicular bisectors. Wait, yes! In a rhombus, the diagonals are perpendicular to each other. So if the angle between the diagonals is \( (6x + 6)^\circ \), then it should be 90 degrees for the diagonals to be perpendicular (since rhombus diagonals are perpendicular). So set \( 6x + 6 = 90 \).

Step2: Solve for x

Subtract 6 from both sides: \( 6x = 90 - 6 = 84 \). Then divide by 6: \( x = \frac{84}{6} = 14 \).

Answer:

14